OF FREQUENCY OF THE BAROMETRIC HEIGHT AT DIVERS STATIONS. 427 
to the meteorology of the British Isles as to illustrate what we believe to be a 
novel method of dealing with barometric frequency, in the hope that it may here¬ 
after be taken up by professed meteorologists having at their disposal trained 
computators. We need not stay to lay stress on the large amount of arithmetical 
work involved in calculating the constants for even the short periods dealt with in the 
present memoir, it will be obvious to any one who has undertaken any statistical 
work of a like character. In order to save a portion of this arithmetical labour, 
a self-recording frequency barometer has been devised by Mr. G. A. Yule, some 
account of which will be found in an Appendix to this paper. We believe that 
with due precautions,* such an instrument would be a valuable addition to tliose 
already in use at the various meteorological stations, and serve for the ready 
calculation of the frequency constants. 
Yet, admitting all the disadvantages of the non-contemporary character and short 
period of some of the data which we have used, we still believe that an examination 
of our diagrams will serve to convince the reader that our method is really capable 
of considerable service. 
Putting aside one or two anomalies, we lind a continuous and gradual change of 
the frequency constants as we pass from station to station round the coast, and it 
appears'as easy to draw the contour lines of equal frequency as it has been hitherto 
supposed to be to draw isobars. 
3. Theory Applied. 
Let y hx be the frequency of a deviation lying between x and x -f Sx from the mean, 
then p,, = S{x’'yBx) S{y^x) may be termed the A'' power of the mean rt*'’ deviation. 
In the case of the Gaussian or normal distribution of the frequency of N observations 
V 27ryU.2 
Here all the odd p,’s vanish and we have the relation ~ I) (2^ ” 3) 
...5.3. l/r/ for the even p’s. In particular p^ = 
When, therefore, the odd p’s are not nearly zero, and the relation p^ = 3/x/ is 
not nearly satisfied, it is impossible on both counts to represent the frequency by a 
normal distribution. 
Let — ppjp^, ^2 — pjpi, then if be not zero and ySg be not equal to three, 
a normal distribution is theoretically impossible. 
Now a skew frequency distribution may be deduced from the skew-binomial {'p-hq)'’ 
as a limit, in the same way as it is possible to deduce the normal frequency dis¬ 
tribution as a limit from the symmetrical binomial -fr ^y. 
* Notably, frequent comparison with the standard nioi'curial barometer. 
3 I 2 
